arXiv subjects

Haoyu Ye

Publications and source records attributed to Haoyu Ye.

3 recordsLinked to original sources

arXiv2026

The Zero Pattern of a Design Matrix Drives Multiple Descent in Over-parameterized Regression

Over-parameterized linear regression has been widely studied over the last decade. However, most existing works assume that the covariates are independent and that their covariance matrices are non-degenerate. In this paper, we relax both assumptions and derive deterministic equivalents for the prediction risk in a vanishing-ridge regime. We show that degeneracy of the covariance matrices and dependence can lead to multiple descent, and characterize where the corresponding peaks can occur. Our proofs use a novel graph representation of the variance profile. We show that maximum matchings and the Dulmage--Mendelsohn decomposition of the associated bipartite graph identify the configurations at which the variance becomes singular.

math.ST↗

arXiv2026

Computable Bounds for Strong Approximations with Applications

The Komlós$\unicode{x2013}$Major$\unicode{x2013}$Tusnády (KMT) inequality for partial sums is one of the most celebrated results in probability theory. Yet its practical application has been hindered by a lack of practical constants. This paper addresses this limitation for bounded i.i.d. random variables. At the cost of an additional logarithmic factor, we propose a computable version of the KMT inequality that depends only on the variables' range and standard deviation. We also derive an empirical version of the inequality that achieves nominal coverage even when the standard deviation is unknown. We then demonstrate the practicality of our bounds through applications to online change point detection and first hitting time probabilities. As a byproduct of our analysis, we obtain a Cramér-type moderate deviation bound for normalized centered partial sums.

math.ST↗

arXiv2024

Poisson approximation for stochastic processes summed over amenable groups

We generalize the Poisson limit theorem to binary functions of random objects whose law is invariant under the action of an amenable group. Examples include stationary random fields, exchangeable sequences, and exchangeable graphs. A celebrated result of E. Lindenstrauss shows that normalized sums over certain increasing subsets of such groups approximate expectations. Our results clarify that the corresponding unnormalized sums of binary statistics are asymptotically Poisson, provided suitable mixing conditions hold. They extend further to randomly subsampled sums and also show that strict invariance of the distribution is not needed if the requisite mixing condition defined by the group holds. We illustrate the results with applications to random fields, Cayley graphs, and Poisson processes on groups.

math.PR↗